Independent Component Analysis [1]} is a widely used model for signal source separation. In order to model signals as latent variables, their distribution cannot be normal because the Gaussian is the most random of all distributions. In fact, according to Jayne’s principle of maximum entropy [2]}, a Gaussian random variable has maximum entropy (i.e.uncertainty) among all random variables with equal variance. In contrast, entropy tends to be small for spiked, or super-Gaussian distributions - distributions that characterize signals!
So if we consider the generalized Gaussian distribution as a prior over the latent variables, we obtain a highly peaked supergaussian distribution (if the shape parameter \(\alpha \)  set to be less than 2) that is appropriate for modeling signals that give rise to sparse data. Note that the version of the generalized Gaussian distribution we are considering is that of parametric symmetric distributions. The normal distribution is a special case obtained when \(\alpha =2\)  and the Laplace distribution is another special case when \(\alpha =1\)  [3]}. ICA can be thought of as a linear latent generative model, a type of a Factor Analysis model but with nongaussian priors over the latent variables (i.e. sources). The model has the following decomposition.
\(\prod _{n=1}^N \mathcal {N}_p( \mathbf {y}_n \mid \mathbf {W}\mathbf {z}_n, \ \operatorname{Diag}(\sigma ^2)) \prod _{n=1}^N \prod _{d=1}^D \mathcal {GG}_d(z_{d,n} \mid \alpha _d) \quad \alpha _d < 2\) 
